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This extends Green's characterization of free and proper transformation groups.
On the other hand, for some equations it is not possible to find a proper transformation.
where Q ij is a proper transformation between two arbitrary orthogonal coordinate systems.
With the proper transformation, the original features could be well represented by a low-dimensional latent variable space.
In contrast, due to the proposed classification along with the proper transformation function, the results of AGC are quite acceptable.
We prove that, under a proper transformation, this inequality is equivalent to the Sobolev inequality in RN.
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The model boundary layer non-linear partial differential equations transform to ODEs by means of proper transformations concerning the geometry of the problem under consideration.
The equations are adjusted to a generic expression by using proper transformations.
The profound alterations that animal spirits can undergo explain the true and proper transformations that occur in someone who has been bitten by a rabid dog or in peasants from Puglia attacked by tarantulas.
All relationships were evaluated graphically, and proper transformations were applied to render them linear.
This laboratory study showed that proper transformations of other task variables can be used to quantitatively predict nearly all of the remaining motion time variance.
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